Contemporary communication systems often employ digital signals to effect communications. In a typical digital communication device, the transmitted source information is represented by a digital information stream. This digital information stream is modulated and amplified for transmission over a communication channel. Many complex digital modulation schemes have been developed to efficiently convey information across a communication channel. For digital modulation, a digital information stream is mapped onto a symbol constellation to generate a sequence of channel symbols.
As is common in with conventional solutions, a symbol constellation for a modulation scheme can be represented graphically as a set of symbols in a two-dimensional structure representing phase and amplitude. The transitions between the successive constellation points denote an exchange of information. In practical use, the transitions between the points are not necessarily in a straight line, but are modified through a trajectory determination circuit. One such trajectory determination apparatus would be a pulse-shaping filter when used in a π/4 QPSK modulation scheme.
FIG. 1 is a constellation diagram of such a system depicting the transition path between the constellation points. In this case, the modulation scheme is a π/4 QPSK modulation. One should note that many possible modulation schemes exist for digital communications, and that depicted in FIG. 1 is exemplary. This disclosure is not limited to the modulation scheme depicted, but should be read as covering all digital communications using constellations.
FIG. 1 is a representation of a channel symbol sequence having values {P0, P1, P6, P7} generated by a channel symbol mapper to represent a sample digital information stream. Note that in this path, the transition moves very close to the origin. Accordingly, the change in the angle between successive points near this minima is rapid. In terms of a broadcast signal, this angle measurement may be used to convey information (i.e. in a frequency modulated (FM) signal, or in other phase modulated systems.)
In the path depicted in FIG. 1, there may be intermediate samples associated with the path. Accordingly, the path as depicted may be made up of various pieces of information. Thus, for any sample in the path depicted in FIG. 1, the sample can be depicted in a form of an ordered pair of amplitude and angle. For low magnitude events, these are almost always characterized by a rapidly changing angle. If the path misses the origin by only a small amount, the change in angle will be greater in amount over a shorter time than for a larger amount. The closer to the origin that the path moves, the rate of change in the angle increases dramatically per unit of time or per sample interval. If the path goes through the origin, the rate of change transitions to an extreme event—an impulse phase shift in the angle (i.e. a discontinuous phase shift in zero time.)
In terms of implementation, the ability of these conventional systems to cope with such rapid changes in this angle measurement may lead to problems within the system. In these cases, many conventional communications systems encounter problems when dealing with the rapidly changing angle, since the components cannot necessarily easily deal with the rapidly changing phase information. Of course, the angle may refer to frequency or phase, depending upon the particular modulation. In the course of this description, the emphasis is on describing the application in terms of phase angle and changes in phase angle. One should note that the values could just as easily describe frequency and changes in frequency, and this description should be read as considering those values as well.
In some conventional solutions, conditioning a low magnitude event requires the definition of a local minima, from which corrections could be made if the signal entered or came close to. However, the associated noise with such solutions varies as the outer border of the defined minima varies. Accordingly, for these conventional solutions the associated noise is dependent upon the defined minima.
Additionally, such conventional solutions typically require corrections in two domains. For example, in some cases an input pulse is added to the entire path when the path encroached on a defined minima. In this case, the correction must be applied to both the coordinate and the ordinate of the path points or samples, as necessary. Further, when adding a pulse in this domain, the typical pulse impacted many points, since by definition the correction is a pulse that is applied to the whole path. Accordingly, these conventional solutions can affect the path or trajectory well outside the range of where they need be.
In yet other conventional solutions, entirely new samples are introduced. This affects the timing characteristics of the particular system. Again, like mentioned above, this may also introduce path effects to large portions of the trajectory.